1  Introduction

SPAMS (SPArse Modeling Software) is an open-source optimization toolbox for sparse estimation with licence GPLv3. It implements algorithms for solving machine learning and signal processing problems involving sparse regularizations.

The library is coded in C++, is compatible with Linux, Mac, and Windows 32bits and 64bits Operating Systems. It is interfaced with Matlab, R and Python, but can be called from any C++ application (by hacking the code a bit).

It requires an implementation of BLAS and LAPACK for performing linear algebra operations. The ones shipped with matlab and R can be used, but also external libraries such as atlas, the netlib implementation, or the Intel Math Kernel Library can be used. It also exploits multi-core CPUs when this feature is supported by the compiler, through OpenMP.

The current licence is GPLv3, which is available at http://www.gnu.org/licenses/gpl.html. For other licensing possibilities allowing its use in proprietary softwares, please contact the author.

Version 2.5 of SPAMS is divided into several “toolboxes” and has a few additional miscellaneous functions:

• The Dictionary learning and matrix factorization toolbox contains the online learning technique of [20, 21] and its variants for solving various matrix factorization problems:
  • dictionary Learning for sparse coding;
  • sparse principal component analysis (seen as a sparse matrix factorization problem);
  • non-negative matrix factorization;
  • non-negative sparse coding;
  • dictionary learning with structured sparsity;
  • archetypal analysis [7, 37].
• The Sparse decomposition toolbox contains efficient implementations of
  • Orthogonal Matching Pursuit, (or Forward Selection) [35, 27];
  • the LARS/homotopy algorithm [30, 9] (variants for solving Lasso and Elastic-Net problems);
  • a weighted version of LARS;
  • OMP and LARS when data comes with a binary mask;
  • a coordinate-descent algorithm for ℓ₁-decomposition problems [12, 10, 36];
  • a greedy solver for simultaneous signal approximation as defined in [34, 33] (SOMP);
  • a solver for simulatneous signal approximation with ℓ₁/ℓ₂-regularization based on block-coordinate descent;
  • a homotopy method for the Fused-Lasso Signal Approximation as defined in [10] with the homotopy method presented in the appendix of [21];
  • a tool for projecting efficiently onto a few convex sets inducing sparsity such as the ℓ₁-ball using the method of [3, 18, 8], and Elastic-Net or Fused Lasso constraint sets as proposed in the appendix of [21].
  • an active-set algorithm for simplex decomposition problems [37].
• The Proximal toolbox: An implementation of proximal methods (ISTA and FISTA [1]) for solving a large class of sparse approximation problems with different combinations of loss and regularizations. One of the main features of this toolbox is to provide a robust stopping criterion based on duality gaps to control the quality of the optimization, whenever possible. It also handles sparse feature matrices for large-scale problems. The following regularizations are implemented:
  • Tikhonov regularization (squared ℓ₂-norm);
  • ℓ₁-norm, ℓ₂, ℓ_∞-norms;
  • Elastic-Net [39];
  • Fused Lasso [32];
  • tree-structured sum of ℓ₂-norms (see [15, 16]);
  • tree-structured sum of ℓ_∞-norms (see [15, 16]);
  • general sum of ℓ_∞-norms (see [22, 23]);
  • mixed ℓ₁/ℓ₂-norms on matrices [38, 29];
  • mixed ℓ₁/ℓ_∞-norms on matrices [38, 29];
  • mixed ℓ₁/ℓ₂-norms on matrices plus ℓ₁ [31, 11];
  • mixed ℓ₁/ℓ_∞-norms on matrices plus ℓ₁;
  • group-lasso with ℓ₂ or ℓ_∞-norms;
  • group-lasso+ℓ₁;
  • multi-task tree-structured sum of ℓ_∞-norms (see [22, 23]);
  • trace norm;
  • ℓ₀ pseudo-norm (only with ISTA);
  • tree-structured ℓ₀ (only with ISTA);
  • rank regularization for matrices (only with ISTA);
  • the path-coding penalties of [24].
  All of these regularization functions can be used with the following losses
  • square loss;
  • square loss with missing observations;
  • logistic loss, weighted logistic loss;
  • multi-class logistic.
  This toolbox can also enforce non-negativity constraints, handle intercepts and sparse matrices. There are also a few additional undocumented functionalities, which are available in the source code. For some combinations of loss and regularizers, stochastic and incremental proximal gradient solvers are also implemented [26, 25].
• A few tools for performing linear algebra operations such as a conjugate gradient algorithm, manipulating sparse matrices and graphs.

The toolbox was written by Julien Mairal at INRIA, with the collaboration of Francis Bach (INRIA), Jean Ponce (Ecole Normale Supérieure), Guillermo Sapiro (University of Minnesota), Guillaume Obozinski (INRIA) and Rodolphe Jenatton (INRIA).

R and Python interfaces have been written by Jean-Paul Chieze (INRIA). The archetypal analysis implementation was written by Yuansi Chen, during an internship at INRIA, with the collaboration of Zaid Harchaoui.